{"id":"https://openalex.org/W2960650218","doi":"https://doi.org/10.1007/s00453-019-00633-1","title":"A Faster Tree-Decomposition Based Algorithm for Counting Linear Extensions","display_name":"A Faster Tree-Decomposition Based Algorithm for Counting Linear Extensions","publication_year":2019,"publication_date":"2019-10-03","ids":{"openalex":"https://openalex.org/W2960650218","doi":"https://doi.org/10.1007/s00453-019-00633-1","mag":"2960650218"},"language":"lv","primary_location":{"id":"doi:10.1007/s00453-019-00633-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-019-00633-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-019-00633-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-019-00633-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043364928","display_name":"Kustaa Kangas","orcid":null},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Kustaa Kangas","raw_affiliation_strings":["Department of Computer Science, Aalto University, Espoo, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088812539","display_name":"Mikko Koivisto","orcid":"https://orcid.org/0000-0001-9662-3605"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Mikko Koivisto","raw_affiliation_strings":["Department of Computer Science, University of Helsinki, Helsinki, Finland"],"raw_orcid":"https://orcid.org/0000-0001-9662-3605","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017404579","display_name":"Sami Salonen","orcid":null},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Sami Salonen","raw_affiliation_strings":["Department of Computer Science, University of Helsinki, Helsinki, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088812539"],"corresponding_institution_ids":["https://openalex.org/I133731052"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.1776,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.5264699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"82","issue":"8","first_page":"2156","last_page":"2173"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7580682039260864},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5407794117927551},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45174455642700195},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.4103090167045593},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3478271961212158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31902092695236206},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15804001688957214},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.08031922578811646}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7580682039260864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5407794117927551},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45174455642700195},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.4103090167045593},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3478271961212158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31902092695236206},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15804001688957214},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.08031922578811646},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00453-019-00633-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-019-00633-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-019-00633-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:aaltodoc.aalto.fi:123456789/41983","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/3ad2a784-e533-4cf5-bea2-d07af2feb68e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401662","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:helda.helsinki.fi:10138/321138","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/321138","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s00453-019-00633-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-019-00633-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-019-00633-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2326707128","display_name":null,"funder_award_id":"316771","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G4607719773","display_name":null,"funder_award_id":"276864","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"}],"funders":[{"id":"https://openalex.org/F4320310086","display_name":"Helsingin Yliopisto","ror":"https://ror.org/040af2s02"},{"id":"https://openalex.org/F4320310467","display_name":"Helsingin ja Uudenmaan Sairaanhoitopiiri","ror":"https://ror.org/020cpqb94"},{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2960650218.pdf","grobid_xml":"https://content.openalex.org/works/W2960650218.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W108487744","https://openalex.org/W1495775210","https://openalex.org/W1557168674","https://openalex.org/W1585310225","https://openalex.org/W1974745849","https://openalex.org/W1982333717","https://openalex.org/W1992058066","https://openalex.org/W2001868457","https://openalex.org/W2002425091","https://openalex.org/W2010953531","https://openalex.org/W2012449655","https://openalex.org/W2047033531","https://openalex.org/W2055916047","https://openalex.org/W2059372025","https://openalex.org/W2061246500","https://openalex.org/W2063342497","https://openalex.org/W2080139830","https://openalex.org/W2085550081","https://openalex.org/W2086886584","https://openalex.org/W2087957223","https://openalex.org/W2110920860","https://openalex.org/W2125058377","https://openalex.org/W2133990480","https://openalex.org/W2231883621","https://openalex.org/W2235897681","https://openalex.org/W2397336691","https://openalex.org/W2540405007","https://openalex.org/W2573381362","https://openalex.org/W2609269940","https://openalex.org/W2617661790","https://openalex.org/W2788914192","https://openalex.org/W2891118272","https://openalex.org/W2920579836","https://openalex.org/W2963807417"],"related_works":["https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2371447506","https://openalex.org/W2365333639","https://openalex.org/W2372769725","https://openalex.org/W2559087450","https://openalex.org/W2365371251","https://openalex.org/W2123016062","https://openalex.org/W2355247546"],"abstract_inverted_index":{"Abstract":[0],"We":[1,25,77,88,124],"investigate":[2,79],"the":[3,7,41,59,62,66,80,91,99,119,141,152],"problem":[4],"of":[5,9,12,58,65,74,86,118,140],"computing":[6],"number":[8],"linear":[10],"extensions":[11],"a":[13,55,83,146,158,173,183],"given":[14],"n":[15,101],"-element":[16],"poset":[17],"whose":[18],"cover":[19,60],"graph":[20],"has":[21],"treewidth":[22],"t":[23,39,103],".":[24],"present":[26],"an":[27,130],"algorithm":[28,50,81],"that":[29,90,176],"runs":[30],"in":[31,111],"time":[32,93,165],"$${\\tilde{O}}(n^{t+3})$$":[33],"<mml:math":[34,44],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mover><mml:mi>O</mml:mi><mml:mo>~</mml:mo></mml:mover><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>":[35],"for":[36],"any":[37],"constant":[38],";":[40],"notation":[42],"$${\\tilde{O}}$$":[43],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mover><mml:mi>O</mml:mi><mml:mo>~</mml:mo></mml:mover></mml:math>":[45],"hides":[46],"polylogarithmic":[47],"factors.":[48],"Our":[49],"applies":[51],"dynamic":[52],"programming":[53],"along":[54],"tree":[56,67,122,132,142,174,186],"decomposition":[57,68,143,175],"graph;":[61],"join":[63],"nodes":[64],"are":[69,169],"handled":[70],"by":[71,98],"fast":[72],"multiplication":[73],"multivariate":[75],"polynomials.":[76],"also":[78],"from":[82],"practical":[84],"point":[85],"view.":[87],"observe":[89],"running":[92,112,164],"is":[94,135,155,178],"not":[95],"well":[96],"characterized":[97],"parameters":[100,107],"and":[102],"alone:":[104],"fixing":[105],"these":[106],"leaves":[108],"large":[109],"variance":[110],"times":[113],"due":[114],"to":[115,128,136,144,156,162,171],"uncontrolled":[116],"features":[117,139],"selected":[120],"optimal-width":[121,185],"decomposition.":[123,187],"compare":[125],"two":[126],"approaches":[127,168],"select":[129],"efficient":[131,181],"decomposition:":[133],"one":[134],"include":[137],"additional":[138],"build":[145],"more":[147,180],"accurate,":[148],"heuristic":[149],"cost":[150],"function;":[151],"other":[153],"approach":[154],"fit":[157],"statistical":[159],"regression":[160],"model":[161],"collected":[163],"data.":[166],"Both":[167],"shown":[170],"yield":[172],"typically":[177],"significantly":[179],"than":[182],"random":[184]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}